Superposition principle and information

In summary, the information about the shapes of the initial waves at this moment of time is stored somewhere.
  • #1
Virous
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I have a question about, perhaps, GCSE level physics, if not below, which, for some reason, is not explained anywhere I've looked up. Or, at least, I didn't find any explanation.

img003.jpg
The picture above is supposed to explain the concept of superposition. It depicts a pair of one-dimensional waves (wave pulses) at 5 different points in time. On the third picture (the exact moment of superposition), the initial individual waves do not exist. Instead we have a single large wave, composed of the energy of both. Where is the information about the shapes of the initial waves at this moment of time stored?

In other words, after the third picture, how does this large wave "know" how it should split in order to restore the initial pulses?

Thank you!
 
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  • #2
Virous said:
On the third picture (the exact moment of superposition), the initial individual waves do not exist.
I think that's where your problem lies. Both waveforms DO exist at that point exactly as they do exist at every other point on the graph, it's just that you are looking at the sum.

If you had a basket of 3 apples and you added 2 more apples, you wouldn't be thinking "damn, where did my 3 apples go? How can I get them out again?" but because the waveforms add in a smooth way, if you ONLY look at the waveform at that point in time, you can't tell what the individual waves look like, whereas with the apples you don't have that problem.
 
  • #3
The apple example would make sense, since apples are composed of different matter (I mean, each apple has its own). The problem with waves, though, is that they are all made of the same matter (the same rope in this case, or whatever that is). So a wave is just a distribution of a particular property (in this case the displacement) in space/time.

When you add two numbers (e.g. 3 and 2) you get 5. If you give 5 to another person, he wouldn't be able to tell, if the original numbers were 4 and 1 or 3 and 2 or 2.5 and 2.5 and so on. This is exactly the same case :)

If you think of it in terms of particles, on the third picture one of the particles is "up" and it is ready to go down. How is that possible that when it goes down it gives unequal amounts of energy to absolutely identical particles on its left and right?

If I were to predict what's going to happen after, I would say that the resulting waves after the superposition would be equal. Yet, all the diagrams draw them in this way, so I'm confused.
 
  • #4
phinds said:
Both waveforms DO exist at that point exactly
If the diagram depicts a real situation, they obviously do :) The question is, where? Particles definitely don't have this information, since they are just particles moving up and down and having a particular displacement function.

Suppose, I have managed to superimpose a million of waves with strange shapes (I guess I would need more dimensions, but anyway). Where will all this information go?
 
  • #5


The superposition principle states that when two or more waves meet, the resulting wave is the sum of the individual waves. This means that the energy of the initial waves is conserved and is still present in the resulting wave. However, the shape and characteristics of the resulting wave will depend on the specific properties of the initial waves, such as their amplitude, frequency, and phase.

In terms of information, the initial waves contain all the necessary information about their individual shapes and properties. This information is preserved in the resulting wave and can be extracted by analyzing its characteristics, such as its amplitude and frequency. So, in the third picture where the two initial waves have combined, the resulting wave contains all the information from the initial waves and can be separated back into its individual components.

To understand this concept further, it may be helpful to think about it in terms of energy and conservation laws. Just like energy is conserved in a closed system, the information about the initial waves is also conserved and present in the resulting wave. The superposition principle allows us to mathematically combine and analyze waves, but the information about their individual properties is still present and can be extracted.
 

What is the Superposition Principle?

The Superposition Principle is a fundamental concept in physics that states that when multiple waves or signals interact with each other, the resulting wave or signal is the sum of the individual waves or signals.

How does the Superposition Principle apply to information?

In terms of information, the Superposition Principle states that multiple pieces of information can coexist and interact with each other without affecting their individual states. This allows for complex systems and networks to function and process information simultaneously.

What is an example of the Superposition Principle in action?

An example of the Superposition Principle in action is in quantum computing. In quantum computers, bits of information, called qubits, can exist in multiple states at the same time, allowing for more complex calculations to be performed simultaneously.

Are there any limitations to the Superposition Principle?

While the Superposition Principle is a fundamental concept in physics, it is not applicable to all systems. In some cases, the interactions between waves or signals may not result in a simple sum, and the principle may not accurately predict the behavior of the system.

How is the Superposition Principle related to quantum entanglement?

Quantum entanglement is a phenomenon where two particles become connected in a way that their states are dependent on each other, regardless of the distance between them. This is possible due to the Superposition Principle, as the particles can exist in multiple states simultaneously until an observation is made, collapsing the superposition and revealing the entangled states.

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